A monopulse antenna system for search and tracking radars includes a plurality of antenna elements designed to receive a signal from a target. In a typical monopulse antenna system, one beam is formed in transmission for search in a specified direction and two or more beams are formed on reception for target detection and angle estimation. A processing schema referred to a maximum-likelihood (ML) target detection and angle estimation makes it possible to reduce or eliminate the beam-shape loss in the received beam thus providing better detection performance and angle estimation accuracy over a large surveillance volume when compared to conventional schema. The plurality of associated antenna elements that define the received beam serve as input to a beamformer which forms various relationships such as: the target detection signal or sum signal rΣ=(I+II+III+IV); an azimuth difference signal rΔAz=(I+IV)−(II+III); and an elevation difference signal rΔEl=(I+II)−(III+IV). FIG. 1 illustrates a plot of the sum and delta beams according to the prior art. In the presence of a target as detected from the sum beam, the elevation difference signal is divided by the sum signal to generate a value to determine the elevation angle of the target, and the azimuth difference signal is divided by the sum signal to generate a value to determine the azimuth angle of the target. The quotients of the division are applied to look up tables in order to determine the corresponding angular location within an antenna beam (see, U.S. Pat. No. 6,404,379, Yu, et al, incorporated herein by reference for a complete explanation of the foregoing monopulse reception scheme).
Technology currently exists to achieve digital beamforming (DBF) at the element or at the sub-array level that serves to provide flexibility in forming multiple received beams, e.g., highly overlapped or squinted sum beams. In this context, maximum-likelihood (ML) estimation schemes have been formulated at the element, the sub-array level and at the beam level.
The ML estimation process entails performing a search over all possible direction of arrival (DOA) of a target return and selecting the direction with a beam weight vector that yields the highest probability of declaring a target to be present. The search can be conducted within a region which is slightly larger then the 3 dB beamwidth of the transmit beam as depicted in FIG. 1. An independent beam search can be performed in every range cell within the range sweep. Thus there will be a set of optimum weights one for each range cell. ML estimation schemes applied at the element level, the sub-array level or beam level require storage of the element pattern or the sub-array pattern or the overlapped sum beam pattern over the beamwidth. Also, an iterative search or a grid search is required for locating the peak of the likelihood function. The ML estimation approach for target detection and angle estimation has a number of advantages (see, E. Kelly, I. Reed and W. Root, “The detection of radar echoes in noise II,” J. Soc. Ind. Appl. Math, vol. 8, pp. 481-510, September 1960).
ML searches over a few beams have been advocated for reducing the computational burden. This approach is called maximum-likelihood beam-space processing (MLBP) (see, R. M Davies and R. L. Fante, “A Maximum-Likelihood Beamspace Processor for Improved Search and Track,” IEEE Trans. Antennas & Propagation, vol. 49, No. 7, July 2001, pp. 1043-1053). This approach also reduces the probability of being stuck in local minima. The MLBP approach divides an antenna into a number of subarrays and digitizes their outputs. The digital signals are then processed in two stages wherein during the first stage the element or sub-array measurements are multiplied by sets of complex weights and summed to form a number of highly overlapped sum beams. The centers of these beams are all within the beamwidth of the transmit beam. During the second stage of processing the beams are weighted and combined to form a single output beam. The beam weights are then chosen to maximize the likelihood of detecting a target return.
MLBP eliminates beam shape loss on receive and increases the volume of space that can be searched for a given number of transmissions. This advantage provides the radar with additional time and energy to perform other functions. The MLBP architecture supports improved angle estimation accuracy compared to monopulse. The MLBP also supports angle estimation over a larger surveillance volume than monopulse. However, there is an increase in demand in terms of both computational and storage requirements. The MLBP requires the beam pattern values of the overlapped beams or the elements or the sub-arrays. It also requires a substantial computational burden when searching over the beamwidth using iterative search or exhaustive grid search methods.
The implementation of a maximum-likelihood target detection and angle estimation in accordance with the present invention can be understood by reference to FIG. 2. Process 200 refers to as element-based or subarray-based ML, whereby digital beamformer (DBF) 210 at the at the element or at the sub-array level creates: gBH(u)=1×N vector of the antenna beam patterns depending on directional cosine u whereby H denotes the complex conjugate transpose; RB=covariance matrix of the set of cluster beams in the form of measurements of the variances plus the correlation measurement; and rB=the measurement of the sum beams. The MLE Angle Estimator 220 computes the likelihood function in accordance with Equation 1 as follows:
                                          Γ            B                    ⁡                      (            u            )                          =                                                                                                                g                    B                    H                                    ⁡                                      (                    u                    )                                                  ⁢                                  R                  B                                      -                    1                                                  ⁢                                  r                  B                                                                    2                                                              g                B                H                            ⁡                              (                u                )                                      ⁢                          R              B                              -                1                                      ⁢                                          g                B                            ⁡                              (                u                )                                                                        (        1        )            
Where:
ΓB(u)=Maximum likelihood target parameter estimator
Again referring to FIG. 2, using essentially the same variables as use in the computation of ΓB(u), a target detection step 230 computes “ŝ” the complex target amplitude and compares the absolute value of “s” to a threshold value to determine if a target has been detected. Equation 2 states:
                              S          ^                =                                                            g                B                H                            ⁡                              (                                  u                  ^                                )                                      ⁢                          R              B                              -                1                                      ⁢                          r              B                                                                          g                B                H                            ⁡                              (                                  u                  ^                                )                                      ⁢                          R              B                              -                1                                      ⁢                                          g                B                            ⁡                              (                                  u                  ^                                )                                                                        (        2        )            
One approach to finding an approximate solution is to hypothesize a dense grid over angle “u” within the main beam receiving antenna pattern and evaluate the ΓB(u) at each location and then choose the angle that corresponds to the maximum. Typically, with this approach a large number of angular locations are required to achieve the desired accuracy. Consequently the grid search implementation is computationally expensive. The requirements for the foregoing prior art element-based or beam-based ML estimation approach are: (a) a storage requirement where all the cluster beam pattern values within the beamwidth with sampling of “u” are sufficiently high for accuracy requirements (the number of storage points is given by: (2× beamwidth/accuracy requirement)); and (b) a computational capacity that performs an iterative search for the maximum with sufficient accuracy or evaluates ΓB(u) at each location and then choose the angle that corresponds to the maximum in over a grid of points with sufficient accuracy. In this prior art beam-based ML estimation approach there are several impediments to the element-based or subarray-based procedure: (1) computational burden, (2) becoming stuck in a local minimum, and (3) excessive storage requirements of all the element or subarray patterns within the beamwidth. As mentioned above, maximum-likelihood beam-space processing (MLBP), which is essentially an ML search over a few beams, has been advocated for reducing the computational burden. This approach reduces the probability of getting stuck in local minima. It has lesser storage requirements, i.e., M beam patterns instead of N element patterns. However, what is needed is an efficient target detection and angle estimation scheme without requiring extensive searching and excessive storage requirement of antenna patterns. The prior art solutions require exhaustive grid search or iterative search over several beams.